Maximum information preservable by supervised continuous ordinal lumping

Calculates the lumping of an ordinal covariate that preserves the maximum Ross-estimated mutual information with a numeric outcome.

Usage

maximum_mutual_information_ordinal_supervised_continuous(
  x,
  y,
  threshold,
  k = 3L
)

Arguments

x

Ordinal covariate. A factor is interpreted in factor level order. Otherwise the sorted unique values are used as the ordinal levels.

y

Numeric outcome vector.

threshold

Minimum number of samples each lumped level must contain.

k

Number of nearest neighbours used by the Ross estimator. Default: 3.

Value

A list containing information about the optimal lumping:

mutual_information

Double representing the Ross-estimated mutual information between the lumped covariate and the outcome.

loss

Double representing the amount of information lost by lumping.

lumping

Integer vector containing the cut points of the optimal lumping, in the same convention as the ordinal discrete implementation.

See also

maximum_mutual_information_ordinal_supervised() for the discrete-outcome version.

maximum_mutual_information_nominal_supervised_continuous() for the nominal analogue.

lump_ordinal_supervised() for a user-friendly wrapper that applies the lumping.

Author

Daan Koning

Examples

set.seed(1)
x <- ordered(rep(c("Low", "Medium", "High"), each = 5),
             levels = c("Low", "Medium", "High"))
y <- c(rnorm(5, 0), rnorm(5, 2), rnorm(5, 4))
maximum_mutual_information_ordinal_supervised_continuous(x, y, threshold = 5)
#> $mutual_information
#> [1] 0.4307968
#> 
#> $loss
#> [1] 0
#> 
#> $lumping
#> [1] 1 2 3 4
#>